Wavelet-domain regression and predictive inference in psychiatric neuroimaging

Annals of Applied Statistics

Volumn 9, Issue 2, 2015, Pages 1076-1101

  Reiss, Philip T ^a   Huo, Lan ^a   Zhao, Yihong ^a   Kelly, Clare ^a   Ogden, R Todd ^b  

^a NEW YORK UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b Columbia University ^*  (United States)

Author keywords

ADHD 200; Elastic net; Functional confounding; Functional regression; Functionalmagnetic resonance imaging; Sparse partial least squares; Sparse principal component regression

Indexed keywords

EID: 84938495493     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/15-AOAS829     Document Type: Article

References (90)

1. ADHD-200 CONSORTIUM (2012). The ADHD-200 consortium: A model to advance the translational potential of neuroimaging in clinical neuroscience. Front. Syst. Neurosci. 6 62.
2. BERLINET, A., BIAU, G. and ROUVIÈRE, L. (2008). Functional supervised classification with wavelets. Ann. I.S.U.P. 52 61-80. MR2435041
3. BROWN, P. J., FEARN, T. and VANNUCCI, M. (2001). Bayesian wavelet regression on curves with application to a spectroscopic calibration problem. J. Amer. Statist. Assoc. 96 398-408. MR1939343
4. BROWN, M. R. G., SIDHU, G. S., GREINER, R., ASGARIAN, N., BASTANI, M., SILVERSTONE, P. H., GREENSHAW, A. J. and DURSUN, S. M. (2012). ADHD-200 global competition: Diagnosing ADHD using personal characteristic data can outperform resting state fMRI measurements. Front. Syst. Neurosci. 6 69.
5. CAFFO, B., ELOYAN, A., HAN, F., LIU, H., MUSCHELLI, J., NEBEL, M. B., ZHAO, T. and CRAINICEANU, C. (2012). SMART thoughts on the ADHD 200 Competition. Available at http://www.smart-stats.org/?q=content/repost-our-document-adhd-competition.
6. CAI, T. T. and HALL, P. (2006). Prediction in functional linear regression. Ann. Statist. 34 2159- 2179. MR2291496
7. CARDOT, H., FERRATY, F. and SARDA, P. (1999). Functional linear model. Statist. Probab. Lett. 45 11-22. MR1718346
8. CARDOT, H., FERRATY, F. and SARDA, P. (2003). Spline estimators for the functional linear model. Statist. Sinica 13 571-591. MR1997162
9. CHANG, C., CHEN, Y. and OGDEN, R. T. (2014). Functional data classification: A wavelet approach. Comput. Statist. 29 1497-1513.
10. CHI, E. C. and SCOTT, D. W. (2014). Robust parametric classification and variable selection by a minimum distance criterion. J. Comput. Graph. Statist. 23 111-128.
11. CHUN, H. and KELEŞ, S. (2010). Sparse partial least squares regression for simultaneous dimension reduction and variable selection. J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 3-25. MR2751241
12. COOK, R. D. (2007). Fisher lecture: Dimension reduction in regression. Statist. Sci. 22 1-26. MR2408655
13. CRADDOCK, R. C., HOLTZHEIMER III, P. E., HU, X. P. and MAYBERG, H. S. (2009). Disease state prediction from resting state functional connectivity. Magn. Reson. Med. 62 1619-1628.
14. CRAINICEANU, C. M., REISS, P. T., GOLDSMITH, J., HUANG, L., HUO, L. and SCHEIPL, F. (2014). refund: Regression with functional data. R package version 0.1-10.
15. DAUBECHIES, I. (1988). Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 909-996. MR0951745
16. DELAIGLE, A. and HALL, P. (2012a). Achieving near perfect classification for functional data. J. R. Stat. Soc. Ser. B. Stat. Methodol. 74 267-286. MR2899863
17. DELAIGLE, A. and HALL, P. (2012b). Methodology and theory for partial least squares applied to functional data. Ann. Statist. 40 322-352. MR3014309
18. DING, B. and GENTLEMAN, R. (2005). Classification using generalized partial least squares. J. Comput. Graph. Statist. 14 280-298. MR2160814
19. DONOHO, D. L. and JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455. MR1311089
20. ELOYAN, A., MUSCHELLI, J., NEBEL, M. B., LIU, H., HAN, F., ZHAO, T., BARBER, A. D., JOEL, S., PEKAR, J. J., MOSTOFSKY, S. H. and CAFFO, B. (2012). Automated diagnoses of attention deficit hyperactive disorder using magnetic resonance imaging. Front. Syst. Neurosci. 6 61.
21. FAN, J. and LI, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581
22. FAY, M. P., KIM, H.-J. and HACHEY, M. (2007). On using truncated sequential probability ratio test boundaries for Monte Carlo implementation of hypothesis tests. J. Comput. Graph. Statist. 16 946-967. MR2412490
23. FRIEDMAN, J.,HASTIE, T. and TIBSHIRANI, R. (2010). Regularization paths for generalized linear models via coordinate descent. J. Stat. Softw. 33 1-22.
24. GOLDSMITH, J.,HUANG, L. andCRAINICEANU, C. M. (2014). Smooth scalar-on-image regression via spatial Bayesian variable selection. J. Comput. Graph. Statist. 8 1045-1064.
25. GOLDSMITH, J., BOBB, J., CRAINICEANU, C. M., CAFFO, B. and REICH, D. (2011). Penalized functional regression. J. Comput. Graph. Statist. 20 830-851. MR2878950
26. GOLLAND, P. and FISCHL, B. (2003). Permutation tests for classification: Towards statistical significance in image-based studies. In Information Processing in Medical Imaging: Proceedings of the 18th International Conference (C. J. Taylor and J. A. Noble, eds.) 330-341. Springer, Berlin.
27. GROSENICK, L., KLINGENBERG, B., KATOVICH, K., KNUTSON, B. and TAYLOR, J. E. (2013). Interpretable whole-brain prediction analysis with GraphNet. NeuroImage 72 304-321.
28. GUILLAS, S. and LAI, M.-J. (2010). Bivariate splines for spatial functional regression models. J. Nonparametr. Stat. 22 477-497. MR2662608
29. HALL, P. and HOROWITZ, J. L. (2007). Methodology and convergence rates for functional linear regression. Ann. Statist. 35 70-91. MR2332269
30. HONORIO, J., TOMASI, D., GOLDSTEIN, R. Z., LEUNG, H.-C. and SAMARAS, D. (2012). Can a single brain region predict a disorder? IEEE Trans. Med. Imaging 31 2062-2072.
31. HUANG, L., GOLDSMITH, J., REISS, P. T., REICH, D. S. and CRAINICEANU, C. M. (2013). Bayesian scalar-on-image regression with application to association between intracranial DTI and cognitive outcomes. NeuroImage 83 210-223.
32. HUO, L., REISS, P. and ZHAO, Y. (2014). refund.wave: Wavelet-domain regression with functional data. R package version 0.1.
33. JOHNSTONE, I. M. and LU, A. Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. J. Amer. Statist. Assoc. 104 682-693. MR2751448
34. KAPUR, S., PHILLIPS, A. G. and INSEL, T. R. (2012). Why has it taken so long for biological psychiatry to develop clinical tests and what to do about it? Mol. Psychiatry 17 1174-1179.
35. MALLAT, S. G. (1989). A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11 674-693.
36. MALLAT, S. (2009). A Wavelet Tour of Signal Processing: The Sparse Way, 3rd ed. Academic Press, Burlington, MA. MR2479996
37. MALLOY, E. J.,MORRIS, J. S., ADAR, S. D., SUH, H., GOLD, D. R. and COULL, B. A. (2010). Wavelet-based functional linear mixed models: An application to measurement error-corrected distributed lag models. Biostatistics 11 432-452.
38. MARX, B. D. (1996). Iteratively reweighted partial least squares estimation for generalized linear regression. Technometrics 38 374-381.
39. MARX, B. D. and EILERS, P. H. C. (1999). Generalized linear regression on sampled signals and curves: A P-spline approach. Technometrics 41 1-13.
40. MARX, B. D. and EILERS, P. H. C. (2005). Multidimensional penalized signal regression. Technometrics 47 13-22. MR2135789
41. MASSY, W. F. (1965). Principal components regression in exploratory statistical research. J. Amer. Statist. Assoc. 60 234-256.
42. MEINSHAUSEN, N. and BÜHLMANN, P. (2010). Stability selection. J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 417-473. MR2758523
43. MEINSHAUSEN, N.,MEIER, L. and BÜHLMANN, P. (2009). p-values for high-dimensional regression. J. Amer. Statist. Assoc. 104 1671-1681. MR2750584
44. MILHAM, M. P. (2012). Open neuroscience solutions for the connectome-wide association era. Neuron 73 214-218.
45. MORRIS, J. S., BALADANDAYUTHAPANI, V., HERRICK, R. C., SANNA, P. and GUTSTEIN, H. (2011). Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data. Ann. Appl. Stat. 5 894-923. MR2840180
46. MÜLLER, H.-G. and STADTMÜLLER, U. (2005). Generalized functional linear models. Ann. Statist. 33 774-805. MR2163159
47. NADLER, B. and COIFMAN, R. R. (2005). The prediction error in CLS and PLS: The importance of feature selection prior to multivariate calibration. J. Chemom. 19 107-118.
48. NASON, G. P. (2008). Wavelet Methods in Statistics with R. Springer, New York. MR2445580
49. NASON, G. (2013). wavethresh: Wavelets statistics and transforms. R package version 4.6.2.
50. NGUYEN, D. V. and ROCKE, D. M. (2002). Tumor classification by partial least squares using microarray gene expression data. Bioinformatics 18 39-50.
51. NICHOLS, T. E. (2012). Multiple testing corrections, nonparametric methods, and random field theory. NeuroImage 62 811-815.
52. OGDEN, R. T. (1997). Essential Wavelets for Statistical Applications and Data Analysis. Birkhäuser, Boston, MA. MR1420193
53. OJALA, M. and GARRIGA, G. C. (2010). Permutation tests for studying classifier performance. J. Mach. Learn. Res. 11 1833-1863. MR2660654
54. ÖZKAYA, S. G. and VAN DE VILLE, D. (2011). Anatomically adapted wavelets for integrated statistical analysis of fMRI data. In 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro 469-472. IEEE, New York.
55. POTTER, D. M. (2005). A permutation test for inference in logistic regression with small- and moderate-sized data sets. Stat. Med. 24 693-708. MR2134534
56. PREDA, C. and SAPORTA, G. (2005). PLS regression on a stochastic process. Comput. Statist. Data Anal. 48 149-158. MR2134488
57. R DEVELOPMENT CORE TEAM (2012). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
58. RAMSAY, J. O. and SILVERMAN, B. W. (2005). Functional Data Analysis, 2nd ed. Springer, New York. MR2168993
59. RASMUSSEN, P.M.,HANSEN, L. K.,MADSEN, K. H., CHURCHILL, N.W. and STROTHER, S. C. (2012). Model sparsity and brain pattern interpretation of classification models in neuroimaging. Pattern Recognition 45 2085-2100.
60. REISS, P. T. (2006). Regression with signals and images as predictors. Ph.D. Thesis, Dept. of Biostatistics, Columbia Univ., New York.
61. REISS, P. T. (2015). Cross-validation and hypothesis testing in neuroimaging: An irenic comment on the exchange between Friston and Lindquist et al. NeuroImage. To appear.
62. REISS, P. T. and OGDEN, R. T. (2007). Functional principal component regression and functional partial least squares. J. Amer. Statist. Assoc. 102 984-996. MR2411660
63. REISS, P. T. and OGDEN, R. T. (2010). Functional generalized linear models with images as predictors. Biometrics 66 61-69. MR2756691
64. REISS, P. T., HUO, L., ZHAO, Y., KELLY, C. and OGDEN, R. T. (2015). Supplement to "Waveletdomain regression and predictive inference in psychiatric neuroimaging." DOI:10.1214/15- AOAS829SUPP.
65. ROSENBAUM, P. R. (2010). Design of Observational Studies. Springer, New York. MR2561612
66. ROTHMAN, K. J. (2012). Epidemiology: An Introduction, 2nd ed. Oxford Univ. Press, New York.
67. RUTTIMANN, U. E., UNSER, M., RAWLINGS, R. R., RIO, D., RAMSEY, N. F., MATTAY, V. S., HOMMER, D. W., FRANK, J. A. andWEINBERGER, D. R. (1998). Statistical analysis of functional MRI data in the wavelet domain. IEEE Trans. Med. Imaging 17 142-154.
68. SABUNCU, M. R., VAN LEEMPUT, K. and ALZHEIMER'S DISEASE NEUROIMAGING INITIATIVE (2012). The relevance voxel machine (RVoxM): A self-tuning Bayesian model for informative image-based prediction. IEEE Trans. Med. Imaging 31 2290-2306.
69. SHEN, H. and HUANG, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. J. Multivariate Anal. 99 1015-1034. MR2419336
70. STONE, M. and BROOKS, R. J. (1990). Continuum regression: Cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression. J. Roy. Statist. Soc. Ser. B 52 237-269. MR1064418
71. SUN, D., VAN ERP, T. G. M., THOMPSON, P. M., BEARDEN, C. E., DALEY, M., KUSHAN, L., HARDT, M. E., NUECHTERLEIN, K. H., TOGA, A. W. and CANNON, T. D. (2009). Elucidating a magnetic resonance imaging-based neuroanatomic biomarker for psychosis: Classification analysis using probabilistic brain atlas and machine learning algorithms. Biological Psychiatry 66 1055-1060.
72. TIBSHIRANI, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267-288. MR1379242
73. VAN DE VILLE, D., SEGHIER, M. L., LAZEYRAS, F., BLU, T. and UNSER, M. (2007). WSPM: Wavelet-based statistical parametric mapping. NeuroImage 37 1205-1217.
74. VIDAKOVIC, B. (1999). Statistical Modeling by Wavelets. Wiley, New York. MR1681904
75. WAND, M. P. and ORMEROD, J. T. (2011). Penalized wavelets: Embedding wavelets into semiparametric regression. Electron. J. Stat. 5 1654-1717. MR2870147
76. WANG, X., RAY, S. and MALLICK, B. K. (2007). Bayesian curve classification using wavelets. J. Amer. Statist. Assoc. 102 962-973. MR2354408
77. WANG, X., NAN, B., ZHU, J., KOEPPE, R. and THE ALZHEIMER'S DISEASE NEUROIMAGING INITIATIVE (2014). Regularized 3D functional regression for brain image data via Haar wavelets. Ann. Appl. Stat. 8 1045-1064.
78. WITTEN, D.M., TIBSHIRANI, R. and HASTIE, T. (2009). A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10 515-534.
79. WOLD, H. (1966). Nonlinear estimation by iterative least square procedures. In Research Papers in Statistics (Festschrift J. Neyman) (F. N. David, ed.) 411-444. Wiley, London. MR0210250
80. YANG, H.,WU, Q.-Z.,GUO, L.-T., LI, Q.-Q., LONG, X.-Y.,HUANG, X.-Q.,CHAN, R. C. K. and GONG, Q.-Y. (2011). Abnormal spontaneous brain activity in medication-naïve ADHD children: A resting state fMRI study. Neurosci. Lett. 502 89-93.
81. ZHAO, Y., CHEN, H. and OGDEN, R. T. (2015). Wavelet-based weighted LASSO and screening approaches in functional linear regression. J. Comput. Graph. Statist. To appear.
82. ZHAO, Y., OGDEN, R. T. and REISS, P. T. (2012). Wavelet-based LASSO in functional linear regression. J. Comput. Graph. Statist. 21 600-617. MR2970910
83. ZHOU, H., LI, L. and ZHU, H. (2013). Tensor regression with applications in neuroimaging data analysis. J. Amer. Statist. Assoc. 108 540-552. MR3174640
84. ZHU, H., BROWN, P. J. andMORRIS, J. S. (2012). Robust classification of functional and quantitative image data using functional mixed models. Biometrics 68 1260-1268. MR3040032
85. ZHU, J. and HASTIE, T. (2004). Classification of gene microarrays by penalized logistic regression. Biostatistics 5 427-443.
86. ZHU, H., VANNUCCI, M. and COX, D. D. (2010). A Bayesian hierarchical model for classification with selection of functional predictors. Biometrics 66 463-473. MR2758826
87. ZOU, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101 1418-1429. MR2279469
88. ZOU, H. and HASTIE, T. (2005). Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B. Stat. Methodol. 67 301-320. MR2137327
89. ZOU, H., HASTIE, T. and TIBSHIRANI, R. (2006). Sparse principal component analysis. J. Comput. Graph. Statist. 15 265-286. MR2252527
90. ZOU, Q.-H., ZHU, C.-Z., YANG, Y., ZUO, X.-N., LONG, X.-Y., CAO, Q.-J., WANG, Y.-F. and ZANG, Y.-F. (2008). An improved approach to detection of amplitude of low-frequency fluctuation (ALFF) for resting-state fMRI: Fractional ALFF. J. Neurosci. Methods 172 137-141.